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April 2008 Estimation of a semiparametric transformation model
Oliver Linton, Stefan Sperlich, Ingrid Van Keilegom
Ann. Statist. 36(2): 686-718 (April 2008). DOI: 10.1214/009053607000000848


This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parameter: maximizing a profile likelihood function or minimizing the mean squared distance from independence. First the problem of identification of such models is discussed. We then state asymptotic results for a general class of nonparametric estimators. Finally, we give some particular examples of nonparametric estimators of transformed separable models. The small sample performance is studied in several simulations.


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Oliver Linton. Stefan Sperlich. Ingrid Van Keilegom. "Estimation of a semiparametric transformation model." Ann. Statist. 36 (2) 686 - 718, April 2008.


Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1133.62029
MathSciNet: MR2396812
Digital Object Identifier: 10.1214/009053607000000848

Primary: 62E20 , 62F12 , 62G05 , 62G08 , 62G20

Keywords: Additive models , generalized structured models , profile likelihood , semiparametric models , separability , Transformation models

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 2 • April 2008
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